ECE 474: Principles of Electronic Devices Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu
Lecture 06: Completed: Chapter 01: quantify physical structures of crystal systems that are important for devices: Cubic systems: bcc, fcc, diamond, zinc-blende Number of atoms in unit cell Lattice constant a Volume density of atoms Packing fraction Nearest neighbor distances lattice-matched compositions for devices Predicted density wafer synthesis from melt Examples of each
Lecture 06: Next: Quantify physical structures of crystal systems that are important for devices: Chapter 01: Cubic systems: bcc, fcc, diamond, zincblende Planes (Miller indices) & directions (orientations) Areal Density Lectures: Hexagonal nanosystems: graphene and carbon nanotubes Unit cell: Chiral and translation vectors Number of atoms Nearest neighbor distances Areal Density Examples of each
Lecture 06: Next: Quantify physical structures of crystal systems that are important for devices: Chapter 01: Cubic systems: bcc, fcc, diamond, zincblende Planes (Miller indices) & directions (orientations) Areal Density Lectures: Hexagonal nanosystems: graphene and carbon nanotubes Unit cell: Chiral and translation vectors Number of atoms Nearest neighbor distances Areal Density Examples of each
Planes and Directions: Motivation: To place a wafer order: O/R: Orientation
What (111), (100) and (110) are: The low index cleavage planes best cuts through the crystal Cleavage plane number of bonds to break. Inside Outside low index break minimum # good cleavage http://www.geo.utexas.edu/cou rses/347k/redesign/gem_note s/diamond/diam_anim.htm Note: If you drop and break a Silicon wafer, lots of sides will have a 35 o angle sides (red lines)
{111} type
{100} type
{110} type
The convention for assigning 1s and 0s to the planes: Miller indices (hkl) First: Clarify a general plane type versus a specific plane: {hkl} versus (hkl)
The {100} generic family of six specific () planes: ( 0 1 0) Left side face ( 100) Front face ( 001) ( 001) Top face Bottom face ( 1 00) Back face ( 010) Right side face p. 08 Streetman
The normal to a plane is its direction or orientation Clarify a general direction type versus a specific direction: <hkl> versus [hkl]
The <100> generic family of six specific [] directions: [ 0 1 0] [ 001] [ 100] [ 010] [ 100] [ 00 1] p. 08 Streetman
Now find the Miller indices (hkl) for the (100) plane. Example: is this a general type or a specific plane?
Now find the Miller indices (hkl) for the (100) plane. Example: is this a general type or a specific plane? Answer: a specific plane. You need a coordinate system.
Miller indices (hkl) for the (100) plane Intercepts reciprocal x lcd =a (hkl) X Y z lcd = least common denominator +z (hkl) = +x +y
Miller indices (hkl) for the (100) plane X Y z Intercepts a reciprocal 1/a 1/ = 0 1/ = 0 x lcd =a 1 0 0 (hkl) 1 0 0 lcd = least common denominator +z (hkl) = (100) +x +y
Find the direction [ ] to the (100) plane.
Direction to the (100) plane [100] +z +x +y
Intercepts reciprocal x lcd =a (hkl) X Y z What ( ) plane was this? lcd = least common denominator +z +x +y
X Y z What ( ) plane is this? Intercepts z 0 reciprocal 1/ 1/ 1/z 0 = 0 = 0 x lcd =z 0 0 0 1 (hkl) 0 0 1 lcd = least common denominator (hkl) = (001) +z +x +y Set origin of coordinate system at bottom and go z 0 up
(111) plane and its direction [ ]
Miller indices (hkl) for the (111) plane X Y z Intercepts a a a reciprocal 1/a 1/ a 1/a x lcd =a 1 1 1 (hkl) 1 1 1 +z lcd = least common denominator (hkl) = (111) +x +y
Direction [ ] to the (111) plane: [111] +z +x +y
(110) plane and its direction [ ]
Miller indices (hkl) for the (110) plane X Y z Intercepts a a reciprocal 1/a 1/ a 1/ = 0 x lcd =a 1 1 0 (hkl) 1 1 0 +z lcd = least common denominator (hkl) = (110) +x +y
Direction [ ] to the (110) plane: [110] +z +x +y
Lecture 06: Next: Quantify physical structures of crystal systems that are important for devices: Chapter 01: Cubic systems: bcc, fcc, diamond, zincblende Planes (Miller indices) & directions (orientations) Areal Density Lectures: Hexagonal nanosystems: graphene and carbon nanotubes Unit cell: Chiral and translation vectors Number of atoms Nearest neighbor distances Areal Density Examples of each
Areal Density: (100) plane Area = a 2 Areal Density 100 = 2.0/a 2 # atoms (cross sections): C 4 (1/4) = 1 F 1 (1) = 1 I 0 (1) = 0 2
Areal Density: (110) plane Area = a 2a = 2 a 2 Areal Density 110 = 4/( 2 a 2 ) = 2.82 / a 2 # atoms (cross sections): C 4 (1/4) = 1 F 2 (1/2) = 1 I 2 (1) = 2 4
Areal Density: (111) plane Equilateral triangle with all sides = 2 a Height = 2 a sin60 o 60 o 60 o 360 o 60 o 60 o Area = ½ base height = ½ ( 2 a) ( 2a sin60 o ) = ( 3/2) a 2 Areal Density 111 = 2 / [( 3/2) a 2 )] = 2.31/a 2 # atoms (cross sections): C 3 (1/6) = 1/2 F 3 (1/2) = 3/2 I 0 (1) = 0 2